The theory of contactmechanics deals with stresses and deformations which arise when the surfaces of two solid bodies are brought into contact. In elastic deformation contact occurs over a finite area. A regular method for determining the dimensions of this area is Hertz Contact Model. Appearance of atomic force microscope results in introduction of ContactMechanics into biology. Low elasticity modulus of biologic particles, causes large deformation against foreign forces, therefore to understand them, studying their behavior is essential. Here, in studying these particles we have used finite element which is a new tool in biology. In this paper indentation of three prostate cancer cells CL -1 , CL -2 and LNCaP which have low elasticity modulus and are considered ductile materials was conducted using Hertz contactmechanics model. For modeling, in this section the contact equations of two spheres were used and simulated by using finite element method (FEM). The results of these two steps were compared with available experimental data on these cells to verify simulations and results. These results include force-displacement diagram which shows particles behavior against foreign load. In this presentation we tried to study the behavior of these cells through different methods and make a comparison. Using finite element approach in studying characteristics of these particles was new.
Since Tatara theory is the expanded model of Hertz theory for hyper-elastic material, the comparison is done between these two models (Figure 7). Biological cells are usually modeled as a visco or hyper-elastic materials. Small deformation contactmechanics models depict that when the nano- particle becomes softer, contact area rises while the applied load declines with sharp slope. But as mentioned before, biological cells are visco or hyper- elastic materials and these kinds of materials have damping properties which does not let the material deform so much due to small forces; it means the force-deformation curve does not have sharp slope. Since Tatara theory as a large deformation model established for a hyper-elastic material, it is simulated for DNA. Results show that using this model the slope of force- deformation curve has slower trend which is closer to the actual situation, so it is suggested to use this model for biological cell. To verify the results obtained for DNA, simulation is done for mESC which experimental curve is available. Results’ comparison in Figure 8 shows that Tatara theory is more compatible with experimental data.
In this paper, a finite element contactmechanics model was presented for simulating the dynamics of a granular chain, subjected to a tone burst excitation. The model was initially validated against results from a discrete mechanics model commonly used to simulate the dynamics of chains of spheres in Hertzian contact. A rigid support was used to terminate the chain in this validation exercise, as this could be replicated in the discrete mechanics model. Good agreement between both models was obtained. The FEA model was subsequently modified to include an accurate model of the termination of the granular chain used in the experiments carried out by Hutchins et al. 11 This termination consisted of an annular support made of a liquid photopolymer resin, rigidly clamped around its outer diameter. The predicted axial component of the velocity of the final sphere of the chain was compared with the laser vibrometer measurement obtained by Hutchins et al. 11 Two types of viscoelastic damping models were implements: one based on velocity proportional damping and another featuring a nonlinear damping coefficient proportional to the square root of the distance of approach between the centers of two adjacent spheres. The former provided good agreement with the experimental waveform both in terms of its time domain and frequency domain characteristics. The finite element model was then extended whereby the granular chain was coupled to a half-space of water via a thin layer of vitreous carbon. Under specific excitation conditions, it was possible to generate frequency content close to 1 MHz with a 73 kHz fundamental excitation signal on the first sphere of the chain.
Results: Results showed that femoral and tibial distal radii, femoral and tibial posterior radii and femoral frontal radius are the most important key parameters which might cause the conflicting impact of geometry on its kinematics and contactmechanics. In the sagittal plane, distal radii of femur and tibia affected both contact pressure and anterior-posterior displacement of the prosthetic components. Also, posterior radii of femur and tibia influenced both contact pressure and internal-external rotation of the prosthetic knee. In the frontal plane, femoral frontal radius influenced both contact pressure and internal-external rotation of the prosthetic components.
The effect of edge loading induced by microseparation on the biomechanics and performance of hard-on-hard articulations has been documented (Manaka et al., 2004; Williams et al., 2006; Leslie et al., 2009; Al-Hajjar et al., 2010). In MoM articulations, edge loading can produce accelerated wear of whole joints (Williams et al., 2006; Leslie et al., 2009) and lead to metallosis, abnormal peri-prosthetic soft-tissue reactions such as pseudotu- mours (Kwon et al., 2012). In CoC combinations, edge loading has been associated with accelerated articulating wear, squeaking, stripe wear on either the head or the cup, and in some situations, the fracture of the components (Nevelos et al., 2001; Stewart et al., 2001; Jarrett et al., 2009; Al-Hajjar et al., 2010). Finite element (FE) studies have also been conducted to examine the stresses in the components due to edge loading and have shown a 3-8 fold increase in the stress of the components in CoC hips compared to that under normal loading conditions (Mak et al., 2002; Sariali et al., 2012). All these studies have provided signi ﬁ cant indication that edge loading due to the rotational and translational malposi- tion of the components has a negative impact on the THRs. However, whilst edge loading has been widely investigated for hard-on-hard articulations, fewer studies have been carried out for hard-on-soft combinations, especially with respect to the contactmechanics of modular MoP THR under microseparation condi- tions. The aim of the present study was therefore to investigate the contactmechanics of a modular MoP THR under edge loading conditions due to the microseparation and rotational malposition- ing of the components using FE methods.
Scapular notching is a common complication of reverse total shoulder arthroplasty (RTSA) wherein the predominant focus of current literature has been on changes in osseous anatomy. However, the implications on RTSA performance from the damaged humeral cup is largely unknown. Therefore the present work describes the effects of the initiation and propagation of the humeral cup defect resulting from scapular notching through the use of finite element modeling and wear simulation, in order to assess changes in RTSA contactmechanics and tribological properties. A significant decrease in articular contact area and increase in maximum contact stress values was found for the tested abduction range of motion for damaged humeral cups. Wear testing of high-mobility RTSA implants indicated a relatively low wear rate, which decreased with the propagation of the scapular notching defect. However, the simulated defect from notching also resulted in a more visibly concentrated secondary wear region within the inferior aspect. Through inferior tilting of the glenosphere, articular contactmechanics were improved, with a significant increase in contact observed, without affecting maximum contact stress values, indicating that this intraoperative parameter may be beneficial beyond the reduced risk for developing scapular notching. Overall, it was indicated that scapular notching damage of the humeral cup may well be detrimental to the assessed articular implant performance parameters, possibly attributing to a decreased lifespan of the implant.
Li, J, Wang, Q, Jin, Z et al. (3 more authors) (2014) Experimental validation of a new biphasic model of the contactmechanics of the porcine hip. Proceedings of the Institution of Mechanical Engineers, Part H: Journal of Engineering in Medicine, 228 (6). 547 - 555. ISSN 0954-4119
and dramatically elevated wear rates 20 in MoM bearings. Sim- ulator tests have also been carried out in an attempt to inves- tigate the effects of head sizes and cup inclination on elevated wear 20,21 under microseparation conditions; these tests have been generally focused on a ﬁxed translation level of 0.5 mm. A full range of parametric studies which can incorporate a wide range of variations in microseparation displacement, cup orientation and cup rim radius are currently not available with simulator tests. These variables are clinically important and relevant, 22,23 and it is not known how they individually or in combination affect contactmechanics or increase wear. Finite element (FE) analysis has been developed to study stripe wear as a result of high contact stresses resulting from head-cup rim contact associated with microseparation for ceramic-on-ceramic (CoC) bearings. 18,24 This method can be further developed for MoM bearings and most importantly extended into an elastic plastic contact analysis in order to predict the high stress. A systematic contactmechanics analy- sis has the potential to predict contact stresses and strains and provide an indication of conditions which could produce the most severe wear.
The aim of this study was to determine the cartilage contactmechanics and the associated fluid pressurisation of the hip joint under eight daily activities, using a three-dimensional finite element hip model with biphasic cartilage layers and gen- eric geometries. Loads with spatial and temporal variations were applied over time and the time-dependent performance of the hip cartilage during walking was also evaluated. It was found that the fluid support ratio was over 90% during the majority of the cycles for all the eight activities. A reduced fluid support ratio was observed for the time at which the contact region slid towards the interior edge of the acetabular cartilage, but these occurred when the absolute level of the peak contact stress was minimal. Over 10 cycles of gait, the peak contact stress and peak fluid pressure remained constant, but a faster process of fluid exudation was observed for the interior edge region of the acetabular cartilage. The results demonstrate the excellent function of the hip cartilage within which the solid matrix is prevented from high levels of stress during activities owing to the load shared by fluid pressurisation. The findings are important in gaining a better understanding of the hip function during daily activities, as well as the pathology of hip degeneration and potential for future interventions. They provide a basis for future subject-specific biphasic investigations of hip performance during activities.
of acoustic signals along a chain of spheres to produce waveforms of relevance to biomedical ultrasound applications. Effects which arise as a result of Hertzian contact between adjacent spheres can potentially change the nature of the signal as it propagates down the chain. The possibility thus exists of generating signals with a different harmonic content to the signal input into one end of the chain. This transduction mechanism has the potential to be of use in both diagnostic and therapeutic ultrasound applications, and is the object of the study presented here. The nonlinear dynamics of granular chains can be treated using discrete mechanics models. However, in cases where the underlying assumptions of these models no longer hold, and where geometries are more complex, a more comprehensive numerical solution must be sought. Contactmechanics problems can efficiently be treated using the finite element method. The latter was used to investigate the dynamics of a pre-stressed chain of six, 1 mm diameter stainless steel spheres excited at one end using a tone burst displacement signal with a fundamental frequency of 73 kHz. The final sphere of the chain was assumed to be in contact with a cylindrical matching layer radiating into a half-space of fluid with the properties of water. After addition of the fluid loading, radiated acoustic pressures in the medium were predicted. Comparison with experimental results suggests that finite element analysis is a suitable tool for investigating the design and performance of contactmechanics based transducers. Nevertheless, a better handle on the model input parameters as well as an improved experimental protocol are required to fully validate the model.
The contactmechanics of polycations and polyanions grafted to an AFM tip with a planar polycationic brush surface have been measured using friction force microscopy. Adhesive interactions demonstrate that the greatest interactions are between the same polycations at high pH and a polycation and polyanion at intermediate pH. The weak interactions between the two polycations at low pH allow the conclusion that hydrogen and van der Waals bonding is largely responsible for the adhesion and electrostatic interactions for the adhesion between oppositely charged polyelectrolytes. The contactmechanics behavior observed for these polyelectrolyte brush systems can be rationalized by treating the friction force as the sum of an area- dependent shear term and a load-dependent plowing term. For highly solvated polycationic brushes, electrostatic repulsions reduce adhesion. Plowing dominates, and the shear term is negligible. As the pH is increased, the polymer becomes less solvated, leading to an increase in the area of contact as the osmotic pressure decreases. As the degree of solvation decreases, the strength of adhesion increases, leading to a transition from behavior consistent with DMT mechanics to behavior that is ﬁ tted by JKR theory. For brushes with dissimilar charges, adhesion reaches a maximum around neutral pH, when electrostatic attractions also reach a maximum.
In this study, the implant stem was cemented into the canal of the radius. This was done to ensure both the quasi-anatomic and patient-specific radial head implants were located in an optimal position. Since, we used a custom stem to fit all implants; the axisymmetric implant was fixed in place as well. Although a fixed position is necessary for anatomically shaped implants, some commercially available axisymmetric implants are designed to have a loose fitting stem or a bipolar head, such that the implant has some ability to self-align the dish against the capitellum (Calfee et al., 2006). During forearm motion the radial heads of these implants may move slightly with respect to the proximal radius such that they stay in optimal contact with the capitellum. Future studies should compare the radiocapitellar kinematics and contactmechanics of anatomically shaped radial head implants to that of a loose fitting stem or bipolar radial head implants.
We systematically elucidate the effects of radial clearance on the wear behavior of hip joint prostheses bearings during run-in-stage. The results indicated that bearings with smaller radial clearances exhibited lower wear rate and less abrasive wear characterized by mild surface roughness and sphericity. The contactmechanics and lubrication regime of MOM bearings with different radial clearances were also analyzed, indicating that bearings with radial clearance of ³ 20 µm was more bene ﬁ cial for small contact pressures even the enlarged clearance made the bearings operate under a full- ﬂ uid-to-mixed lubrication during wear. The agreement between the experimental results of wear rate (mm 3 / Mc)
The impact of a pipe onto a concrete wall is an important problem in the structural integrity assessment of nuclear power plants. The problem assumes that a pipe, cantilevered at one end, experiences a guilotine break at the other end that creates transverse hydrodynamic forces, which cause the pipe to whip into a nearby concrete wall. The interaction between the wall and the pipe is taken into account by using contact elements. The FE model is shown in Fig. 2a. Quadrilateral reinforced concrete plate elements are used to model the wall; pipe elements are used to model the pipe; and and point-to-line contact elements are used to model the contactmechanics. The boundary conditions for the wall do not allow translation but do allow rotations. Because the point-to-line contact element was used, the pipe was constrained to move in the x-y plane. At the guilotine end of the pipe, a hydrodynamic force is applied perpendicular to the pipe; this is the force that drives the pipe into the reinforced concrete wall. Note, for the first study the force is assumed constant and remains on througthout the simulation. The FE analyses were performed using the NEPTUNE  structural analysis software. The deflection-time histories for the pipe and gap between wall and elbow are shown in Fig. 2b.
The work carried out by Hutchins et al  was used as a starting point for the dynamic analysis described in this paper. The granular chain consists of six spherical chrome steel beads. It was assumed that no pre-compressional static force was acting along the axis of the chain, so that the beads were just touching. Although this situation implies that no acoustic waves can propagate up and down the chain, it is known to lead to highly non-linear behaviour , which is more likely to generate signals relevant to biomedical ultrasound , . All FEA was carried out using ANSYS TM Mechanical version 15. The beads were assumed to be perfectly aligned, so that an axisymmetric analysis could be opted for, whereby the Cartesian y-axis defined the axis of symmetry of the granular chain, and the analysis was carried out in the x-y plane. The first bead of the chain was excited via a cylindrical piston whose degrees of freedom were coupled to ensure rigid body motion. A rigidly vibrating piston was employed to reduce uncertainties when comparing with the discrete mechanics model in  and , since modelling semi-infinite structures using FEA presents challenges. For similar reasons, the final bead of the chain was assumed to be in contact with a rigid support. All contacts were assumed to be frictionless, thus simulating Hertzian contacts. The introduction of a linear viscous damping coefficient between successive spheres, as proposed in , was not implemented as part of this work. Again, including this type of damping in the FEA model would add a layer of complexity to the validation process. Hence, dissipative mechanisms will be neglected here and dealt with in a separate paper.
Previous work on FFM has, with few exceptions, used a single medium or a small number of media, making it di ﬃ cult to draw reliable correlations between interfacial behavior and liquid properties. In recent work in the authors ’ laboratory, adhesion forces were measured between carboxylic acid functionalized SAMs in liquid mixtures containing a hydro- carbon (heptane) and a hydrogen bond acceptor (acetone or ethyl acetate). 17 It was found that the variation in the adhesion force F a as a function of the composition of the liquid medium correlated closely with the variation in the free energy of interaction between carboxylic acids, and yielded a value for K S , the association constant between the carboxylic acid group and the hydrogen bond acceptor in the liquid medium, that was in very close agreement with calculated values (con ﬁ rmed in the bulk phase by spectroscopic measurements). It was found that a linear friction-load relationship was observed under conditions where there was extensive (almost complete) solvation of the SAM surface by the solution-phase hydrogen-bond acceptor, while DMT mechanics were observed in other circumstances. These ﬁ ndings were rationalized by postulating that the friction force could be treated, as others have suggested, 2,18 as the sum of a load-dependent term and a surface shear term: 17,19
(P3) Radial approximation or space-time separation. Unknown ﬁelds are represented as a sum of products between a space function and a time function to limit memory usage. An orthonormality condition is prescribed for space modes (i.e. left vectors). For certain cases and for a sake of simplicity, the LATIN method can be formulated without the space-time separation (i.e. the solution is not sought into a low rank approximation). In this case several similarities can be stated with augmented Lagrangian methods . All in all, the LATIN method for frictional contact problems consists in global / local strategy whose global stage does not require matrix re-factorization (stiﬀness operator remains constant along LATIN iterations, symmetric and deﬁnite positive) and local stage is explicit (no iterations are required to handle the non-linear behavior at the contacting boundary). As a consequence, comparisons between LATIN and Newton solvers is not an easy task as the number of iterations is not a good performance indicator for possible comparison. Only CPU measures seem a good approach for that purpose.